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Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by Means of the Porod Invariant from SAXS J. Liu,† S. Pancera,‡ V. Boyko,‡ A. Shukla,§ T. Narayanan,§ and K. Huber*,† †
Chemistry Department, Universit€ at Paderborn, Warburger Strasse 100, D-33089 Paderborn, Germany, BASF SE, Polymer Physics, 67056 Ludwigshafen, Germany, and §European Synchrotron Radiation Facility, F-38043 Grenoble, France
‡
Received May 12, 2010. Revised Manuscript Received September 30, 2010 A time-resolved SAXS study has been carried out on the formation of amorphous calcium carbonate from supersaturated aqueous solutions at an initial concentration of 5 mmol/L CaCO3. Particle formation was induced by mixing equal volumes of equinormal CaCl2 and Na2CO3 solutions with a stopped-flow device installed at the SAXS beamline. The resulting scattering curves were analyzed without any model assumption with respect to the particle shape. The analysis is based on the intercept of the scattering curve, its initial slope, and the Porod invariant. These parameters give access to the average particle mass, the average particle size, and the mass concentration of the particles, respectively. The evolution of particle mass and concentration with time gives access to the trend in the particle number density. The size and mass values were found to be correlated by characteristic exponents. Two different mass values can be used for this correlation: direct use of the intercept of the scattering curve or alternatively a ratio of this intercept with the corresponding Porod invariant. The resulting exponents depend on the particle growth mechanism. These exponents, together with the evolution of the number density, are capable of discriminating between a monomer-addition mechanism and a particle-particle coagulation mechanism as two alternative building mechanisms for the resulting amorphous CaCO3 nanoparticles. A detailed description of the data analysis and its merit in establishing a particle growth mechanism is presented.
Introduction The formation of calcium carbonate from supersaturated solution is a ubiquitous chemical process both in nature and in technical applications. In nature, this process is an important aspect of biomineralization and leads to high-performance materials such as those in the exoskeleton of molluscs or the spines of sea urchins.1 Unlike with biomineralization, calcium carbonate formation frequently turns into a highly undesirable side reaction once hard water is involved in technical processes such as household laundry or the circulation of hot water in pipe systems.2,3 Therefore, a detailed understanding of calcium carbonate formation is highly desirable because it may serve as a source of inspiration for the development of new high-performance materials or it may help to better control or even prohibit it in technical applications. At least four different polymorphs exist for solid CaCO3, including amorphous calcium carbonate (ACC), vaterite, aragonite, and calcite. Under ambient conditions, the stability of the crystalline polymorphs increases along the sequence vaterite, aragonite, and calcite. Thermodynamically, the least stable modification is ACC.4,5 The trend in solubility of the modifications varies inversely with the respective thermodynamic stability of the modification. This increasing order of metastability observed for a series of polymorphs with comparable stability within a given material follows the order of decreasing surface energy, which usually decreases with decreasing density. The trend in metastability is caused by an interplay of the surface energy and bulk energy and appears below a certain particle size. As a consequence, (1) Gower, L. B. Chem. Rev. 2008, 108, 4551–4627. (2) Richter, F. H.; Winkler, E.; Baur, R. H. J. Am. Oil Chem. Soc. 1989, 66, 1666–1672. (3) Rieger, J.; H€adicke, E.; Rau, I. U. Tenside, Surfactants, Deterg. 1997, 34, 430. (4) Brecevic, L.; Nielsen, A. E. J. Cryst. Growth 1989, 98, 504–510. (5) Clarkson, J. R.; Price, T. J.; Adams, C. J. J. Chem. Soc., Faraday Trans. 1992, 88, 243–249.
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the stable modification is approached via the Ostwald-Volmer rule by passing intermediate phases with decreasing metastability.6 Rieger et al. could clearly demonstrate that the initially formed ACC gradually transforms into stable calcite crystals via the state of dissolved ions in equilibrium.7 The disappearing ACC exhibited a granular structure with constituent ACC particles smaller than 100 nm. The addition of polyacrylate chains led to the stabilization of ACC nanoparticles, supporting the assumption of small precursor particles. A considerable step forward in the understanding of the ACC formation was provided by Ballauff et al., who published a series of striking time-resolved small-angle X-ray scattering experiments.8-10 Using a stopped-flow device, they succeeded in providing a series of captivating scattering curves with clear-cut evidence for spherically shaped particles with an extremely narrow size distribution. A straightforward application of model fits based on regular spheres with a finite size distribution gave evidence for a short period of nucleation that led to a constant number of growing particles. The CaCO3 level covered a regime of 3.5 mM e [CaCO3] e 4.5 mM. In all cases, an intermediate species with a constant particle size was achieved. The size of these metastable particles increased with the initial concentration of CaCO3.8 If this carbonate content was set to [CaCO3] = 10 mM, then the particle distribution became broader. Results in the latter case indicated particles with a radius of 19 nm as basic constituents, which successively form larger aggregates.10 The density of 1.62 g/cm3, which is low compared to the densities of the three crystalline polymorphs, confirmed the (6) Navrotsky, A. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 12096–12101. (7) Rieger, J.; Thieme, J.; Schmidt, C. Langmuir 2000, 16, 8300–8305. (8) Bolze, J.; Peng, B.; Dingenouts, N.; Panine, P.; Narayanan, T.; Ballauff, M. Langmuir 2002, 18, 8364–8369. (9) Pontoni, D.; Bolze, J.; Dingenouts, N.; Narayanan, T.; Ballauff, M. J. Phys. Chem. B 2003, 107, 5123–5125. (10) Bolze, J.; Pontoni, D.; Ballauff, M.; Narayanan, T.; C€olfen, H. J. Colloid Interface Sci. 2004, 277, 84–94.
Published on Web 10/20/2010
DOI: 10.1021/la101888c
17405
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Liu et al.
amorphous nature of the particles.8 If combined with wide-angle X-ray scattering, the same authors could unambiguously demonstrate that ACC is transformed into the thermodynamically stable calcite modification via dissolution and subsequent crystallization of the constituent ions,9 in close agreement with the earlier findings by Rieger et al.7 Another interesting aspect of the mechanism of ACC formation was disclosed by Wegner et al.,11 who provided evidence for the occurrence of a spinodal decomposition with a lower critical solution temperature of Tc = 10 C. They applied an in situ generation of the CO32- ions by means of the hydrolysis of dialkyl-carbonates. This ester hydrolysis requires a significant lag time to produce enough CO32- ions and thus avoided inhomogeneities, which inevitably occur during the initial stages of any mixing of component solutions and may interfere with nucleation. The latest piece in a puzzle was recently provided by C€olfen et al.12 by means of a carefully performed analysis of the Ca2þ ion concentration while titrating a large excess of Na2CO3 solution with small increments of a CaCl2 solution. The application of a Ca2þ-sensitive electrode detected only a constant fraction of the total number of Ca2þ ions added until nucleation sets in. This is compatible with the equilibrium between Ca2þ ions in the solution state and a cluster species of CaCO3 during the whole prenucleation phase. One issue that is still a matter of debate refers to the growth mechanism of ACC nanoparticles after nucleation and can be stated as follows: does the growth mechanism proceed with the coalescence of ACC particles with an ever increasing average size, or does growth follow a “monomer”-addition step? The present work will give a clear answer to this question without being able to specify the term monomer, which may correspond to constituent ions, molecular CaCO3 units or clusters such as those identified by C€olfen et al.12 The answer is provided by an analysis of the scattering curves performed without any model assumptions made about the shape of the particles. It simply takes advantage of the accessibility of the so-called Porod invariant.13 The approach uses this invariant to establish particle mass values and number densities of the growing particles in solution and successively correlates the resulting mass and size parameters, thereby providing unambiguous indications for the particle-formation mechanism.
Experiments and Data Reduction Materials. Calcium chloride hexahydrate CaCl2 3 6H2O (assay g99%) and sodium carbonate Na2CO3 (assay g99%) were purchased from Fluka (Buchs, CH). Sodium hydroxide (assay g99%) was supplied by Merck (Darmstadt, FRG). Doubly distilled water (conductivity
